Linear Function Review

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation f(x) = mx + b.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value). If any x-value is paired with more than one y-value, it is not a function.

Front

What is point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the x-value into the function's equation and solve for f(x).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the x-values increase, the y-values decrease. This is indicated by a negative slope.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase. This is indicated by a positive slope.

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.